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[美]布莱兹尼阿克、[美]扎斯塔尼阿克 著 / 清华大学出版社 / 2009-11 / 平装
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上书时间2020-04-01
Springer大学数学图书:随机过程基础(影印版)
随机过程在数学、科学和工程中有着越来越广泛的应用。《随机过程基础》包括随机过程一些基本而又重要的内容:条件期望,Markov链,Poisson过程和Brown运动;同时也包括Ito积分和随机微分方程等应用范围越来越广的内容。《随机过程基础》的习题是其基本内容的延伸,而且有十分完整的解答,非常适合高年级本科生和研究生自学使用或用作教学参考书。
1.ReviewofProbability1.1EventsandProbability1.2RandomVariables1.3ConditionalProbabilityandIndependence1.4Solutions2.ConditionalExpectation2.1ConditioningonanEvent2.2ConditioningonaDiscreteRandomVariable2.3ConditioningonanArbitraryRandomVariable2.4Conditioningonaa-Field2.5GeneralProperties2.5VariousExercisesonConditionalExpectation2.7Solutions3MartingalesinDiscreteTime3.1SequencesofRandomVariables3.2Filtrations3.3Martingales3.4GamesorUhance3.5StoppingTimes3.5OptionalStoppingTheorem3.7Solutions4MartingaleInequalitiesandConvergence4.1DoobsMartingaleInequalities4.2DoobsMartingaleConvergenceTheorem4.3UniformIntegrabilityandL1ConvergenceofMartingales4.4Solutions5.MarkovChains5.1FirstExamplesandDefinitions5.2ClassificationofStates5.3Long-TimeBehaviourofMarkovChains:GeneralCase5.4Long-TimeBehaviourofMarkovChainswithFiniteStateSpace5.5Solutions6.StochasticProcessesinContinuousTime6.1GeneralNotions6.2PoissonProcess6.2.1ExponentialDistributionandLackofMemory6.2.2ConstructionofthePoissonProcess6.2.3PoissonProcessStartsfromScratchatTimet6.2.4VariousExercisesonthePoissonProcess6.3BrownianMotion6.3.1DefinitionandBasicProperties6.3.2IncrementsofBrownianMotion6.3.3SamplePaths6.3.4DoobsMaximalL2InequalityforBrownianMotion6.3.5VariousExercisesonBrownianMotion6.4Solutions7.ItoStochasticCalculus7.1ItoStochasticIntegral:Definition7.2Examples7.3PropertiesoftheStochasticIntegral7.4StochasticDifferentialandIt5Formula7.5StochasticDifferentialEquations7.6SolutionsIndex
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